Falah Abu Maria, 50, was shot in the chest in the village of Beit Omar near the southern city of Hebron, neighbours said.
He had run downstairs at his home to see what was happening when troops stormed it to arrest his son Mohammed, they added. The hospital said that the 24-year-old son was being treated for a gunshot wound to the pelvis.
An Israeli army spokeswoman said that during the raid to detain Mohammed, wanted on suspicion of security offences, "forces were attacked by a violent mob."
She said that one man attacked a soldier, who in response shot him in a lower limb. The wounded man was taken to hospital, she said. The spokeswoman could not confirm his identity but acknowledged that the wanted suspect was not taken into custody.
"As the forces left the scene, they were attacked once again by a violent mob who hurled rocks and bricks at them," she added. "The forces responded with fire towards the main instigator."
She said that a soldier was "slightly injured" by the stone-throwing.
The incident was similar to one on Wednesday near the northern West Bank city of Jenin, where troops shot dead Mohammed Alawneh, 22, in clashes that followed raids and searches at several houses in the village of Birqin.
Alawneh was shot in the chest and died shortly after arriving at hospital in Jenin, a Palestinian medic said. Israeli authorities say such raids are necessary to detain suspects and that troops can face dangerous rioting during the operations.
Palestinians, however, condemn the raids in the occupied territories, and the Hamas and Islamic Jihad militant groups hinted at revenge after Thursday's death.
"We hold the Zionist occupation's forces totally responsible for the killing of the martyr Falah Abu Maria in cold blood," they said in a joint statement.
"The two movements stress our people's right to self-defence and to a response to the crimes of the occupation, by all possible and available means."
The shootings came after weeks of low-level violence in the occupied Palestinian territories, and amid regular Israeli arrest operations.
The recent deaths "aim to undermine stability and to create a climate of tension in the region," official Palestinian news agency Wafa quoted president Mahmud Abbas's spokesman as saying. "Stop creating this damaging climate immediately," he added, referring to Israel.
Last month, soldiers shot dead a Palestinian who opened fire at troops at a checkpoint in the Jordan Valley during the Muslim fasting month of Ramadan.
Also in June, a Palestinian stabbed an Israeli policeman in Israeli-annexed east Jerusalem's Old City, before being shot and wounded.
Last week, Israel arrested five Palestinians suspected of involvement in the murder of an Israeli who was shot in his car in the occupied West Bank.
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